I was reading some Bertrand Russell and he casually mentioned that according to some nominalists, numbers are only useful fictions, and that there are no real particulars. And that left me confused. How can numbers be anything but computation? How can models be anything other than the domain of minds? (computers).
I'm not a Platonist, but I'm not a pure empiricist either. I think that arriving at truth is possible in a rationalist sense, but only of events which require no evidence. In this way, I view math and logic as pure computation which requires a mind.
I don't even understand what it means to say that math can be independent of a mind, so I find it difficult to phrase the question in the title correctly. Saying that there is computation independent of a computer sounds like a white black, a North South, an existent nothing, or a left right.
I don't mean to say that the universe is not ordered in a predictable way that can be understood through mathematics.
I mean, how can there possibly be numbers, values, or computation independent of minds?
I'm really only interested in hearing of examples of math independent of minds. (no matter how complicated or difficult the example is, though I'd prefer the example is presented in its simplest form for my own limited understanding and for the sake of discussion.)
Sell it to me, user. Convince me to spend my time-money on your word-products. I'm a highly discerning ideas-consumer and frugality and shrewdness are part in parcel with that.
Julian Collins
>make a computer run Coq >don't look at it >????? >math independant of a mind
James Jenkins
If you understand something I do not, and have the time to impart that knowledge with the rest of us, doing so would be generous which is what a self-actualized person generally strives to be.
If you are not only a discerning ideas-consumer but also a wise man, you know that another desires the knowledge you have presumably to put it to good use. If you value that end, sharing it with him would be putting that knowledge to good use on your own part. -- If you don't value that end, I lose nothing since I have nothing else to offer but what you don't value.
Although if you do have the knowledge I seek and you're willing to part with it, I could manage to give you a compliment.
Thomas Howard
>part in parcel you sound like my Grandpa, except less literate
Carson Baker
It's an old southern or English dialect. I like it because it's full of janky phrases like "dull as ditchwater," and it reminds me of home.
Gavin Rogers
>I don't even understand what it means to say that math can be independent of a mind, so I find it difficult to phrase the question in the title correctly. Saying that there is computation independent of a computer sounds like a white black, a North South, an existent nothing, or a left right.
It just means you're ontologically committed to the reality of mathematical entities and mathematics as a descriptive endeavor. Which in English means you're subscribing to the idea that the mind can make contact with an absolute mathematical reality which exists over and above human thought. It's up to you and your own metaphysical prejudices
Benjamin Russell
Oh look, another lengthy block of text begging for more free handouts of valuable user attention.
Look, I don't know where you're from, but these servers are in America, buddy. Home of the free doesn't mean home of the free shit readily handed to you by complete strangers on the Internet. Listen- LISTEN- I'm trying to help you. But you gotta help me. So take that novel you posted, condense it down into some configuration of no more than 15 syllables, and post it with a picture of a puppy so that I have something to look at between words.
You're welcome.
Brayden Gray
>the reality of mathematical entities and mathematics as a descriptive endeavor.
Well which is it? Are mathematical entities a reality or descriptive endeavors?
>the idea that the mind can make contact with an absolute mathematical reality which exists over and above human thought.
What does that mean? If it's over and above our thought, how can we make contact with it? Is it a mind or isn't it?
As I said in the OP, my prejudices are mostly as a dogmatic empiricist. Though I recognize and appreciate rationalism, I find it hard to understand why people subscribe to the idea that there are math ghosts that whisper to us, over the very simple idea that we just evolved rational tools to understand a rational universe.
Correct me if I'm wrong, sincerely, but it seems that rationalists are advocating that examining the tools we have evolved to understand a rational universe will somehow explain rationality in the universe. -- As if examining a clay pot will explain the nature of the water it's supposed to hold.
Please, help me make sense of this!
Justin Cruz
If you have anything worthwhile to share you will because you want to help people and put your knowledge to use.
>I'm a highly discerning ideas-consumer >spends his time on Veeky Forums
Kevin Phillips
If math falls in a forest and there are no sapient observers to interpret it, did it prove Pythagoras' Theorem?
Gabriel Green
>I don't even understand what it means to say that math can be independent of a mind
There are mathematicians who have written books claiming this to be the case. That mathematics is the substructure of the universe itself or some such.
Josiah Roberts
Before humans, there was one plant. Then two. Then three. No one was there to think about it.
Robert Torres
But that's kind of begging the question. If math is independent of minds, then what is it one is referring to when one refers to math?
As far as I can figure, like geometric points in space or abstract ideals, it is supposed that there is a divine abstract model that exists. But this divine model can only be supposed.
--- Let me refine my question. Can math ever be anything other than descriptive? if so, do you have an example? If not, who is doing the describing without a mind to compute the description?
David Murphy
>How can numbers be anything but computation?
I don't understand what this means. When I think of a number, I image the digits of the number represented using arabic numerals in my head. Sometimes, when the number x is small, I can think of some configuration of x objects (usually dots or sticks or whatever) in my head.
Mason Campbell
all of that requires computation. To imagine "1" as in contrast with "0" requires computation.
Jaxson Williams
I don't know what you mean by "computation". Are you regarding brains as computers?
Hudson Wright
Yes, brains do compute. Do you not regard them as computers?
David Hall
No. In all models of computation, repeating the same input will produce the same output. Brains don't behave this way because of feedback.
Cameron Thomas
True, part of the brain does not behave this way. That's why logicians had need to invent intuitionist and fuzzy logic.
Otherwise, How is it the brain is able to compute? Given the same input variables and correctly ordered thinking, a brain should always produce the same output. Isn't that what computation is?
Zachary Campbell
>If math is independent of minds, then what is it one is referring to when one refers to math?
dude, stfu
Ian Rogers
>logicians had need to invent intuitionist and fuzzy logic.
>Given the same input variables and correctly ordered thinking, a brain should always produce the same output. Isn't that what computation is?
That is deterministic computation.
Josiah Evans
But just said:
>In all models of computation, repeating the same input will produce the same output.
If that is deterministic computation, what models of computation are there that are non-deterministic?
my mistake. Thank you for your correction.
Kevin Myers
>If that is deterministic computation, what models of computation are there that are non-deterministic?
Non-deterministic Turing Machines. Literally do a Google search, it takes 2 seconds. Do we have to spoonfeed you everything?
Charles Sullivan
>In all models of computation, repeating the same input will produce the same output. Not all models of computation are like this. Examples: probabilistic and quantum models of computation do not yield the same output for the same input.
Gabriel Butler
After reading the wiki entry non non-deterministic turing machines, I'm left unsatisfied.
From my understanding of the theoretical machine, it models a mind. The internal state of the machine computes things in a deterministic way, right?
Regardless, I'm still left puzzled about how some people theorize that math can exist independent of a computer. (a brain or otherwise.)
Henry Watson
i misspoke
*is only able to be modeled by a mind*
Dominic Peterson
>math can exist What does this even mean? I don't think existence is a property of math.
Juan Allen
Don't expect mathematically illiterate philosophers to be able to define what they're talking about. If they could they would just do math.
Jason Collins
But that's exactly my question. How is it that some philosophers suppose that math exists? What does that even mean?
Be as snide as you'd like, I have no ego. I am only interested in answers.
